Regular Black Hole Interior Spacetime Supported by Three-Form Field

TL;DR

This paper demonstrates that a minimally coupled 3-form field with a suitable potential can support a regular, singularity-free black hole interior, replacing the singularity with a Nariai-type spacetime and offering insights into de Sitter geometry origins.

Contribution

It introduces a novel model where a 3-form field supports a regular black hole interior with a Nariai-type spacetime, avoiding singularities and suggesting a mechanism for dynamical compactification.

Findings

The black hole interior is regular and geodesically complete.

The singularity is replaced by a Nariai-type spacetime with topology dS2 x S2.

The interior geometry exhibits dynamical compactification despite negative potential.

Abstract

In this paper, we show that a minimally coupled 3-form endowed with a proper potential can support a regular black hole interior. By choosing an appropriate form for the metric function representing the radius of the 2-sphere, we solve for the 3-form field and its potential. Using the obtained solution, we construct an interior black hole spacetime which is everywhere regular. The singularity is replaced with a Nariai-type spacetime, whose topology is $\text{dS}_2 \times \text{S}^2$, in which the radius of the 2-sphere is constant. So long as the interior continues to expand indefinitely, the geometry becomes essentially compactified. The 2-dimensional de Sitter geometry appears despite the negative potential of the 3-form field. Such a dynamical compactification could shed some light on the origin of de Sitter geometry of our Universe, exacerbated by the Swampland conjecture. In addition, we show that the spacetime is geodesically complete. The geometry is singularity-free due to the violation of the null energy condition.